It makes sense that Fitzgerald's words could be applied to the rap genre. There are different approaches to take with this. Capturing Nick's admission about his own apparent honesty could be done in a very direct manner:
Everybody's got their own view of their own vibe
This I know is mine.
While others might have their own virtues cardinal.
My honesty and truth is what I consider essential.
This is the most basic read of the line. It takes the closing of chapter three and simply puts it in a direct rhyming manner. A strong baseline to this would enable the words to flow fairly well in a freestyle rap. It takes some of the context in the closing paragraph of chapter three and puts in a quatrain.
Another example would be to expand it a bit and take some of the paragraph above when Nick is talking about Jordan. From this discussion of Jordan, Nick is able to talk about others and how he views himself in such a light. Doing this enables another rap version of Nick's insights:
I carry myself as slow thinking- need to put a brake on my desire.
I watch and see others go through theirs like they on fire.
Slow thinking and deliberate is how I live, and this makes me alone.
I know that I am one of the few honest people that I have ever known.
This rap takes some of the ideas from the second to last paragraph. It also pivots to Nick's view of society, in particular Jordan. Seeing that Nick's reliability as a narrator is a significant subtext in Fitzgerald's story, it might be interesting to see him rap about how different he is from others.
In many regards, rap allows the individual to distinguish themselves from others. If one wanted to take a stronger stance on how "different" Nick might see himself from others, using the language that Fitzgerald creates might yield something different:
Seeing gowns in gas blue with lavender, looking good to the feel
Sycophantic suck ups with no idea of what is real
Gatsby smiles to others, but I can see he is alone.
I am one of the few honest people I have ever known
Addressing one of the major themes in rap music that there is a difference between what is and what should be, this vision of Nick hardens the difference between himself and those around Gatsby. This stance is seen in full force towards the end of the novel, but it takes the opulence of the chapter and brings out the loneliness in Gatsby and Nick's commitment to his honesty in the midst of such a dynamic.
Finally, I think that the idea of Nick and Jordan could be an interesting rap. The ending to chapter three is one where Nick brings out this contrast, so freestyling about their difference is not such a stretch:
Seeing that fake mustache of perspiration on her brow
While she lies and acts different from what she says, I know I am down
I hear her saying stuff that I know ain’t real
I am one of the few honest people I know, something I know is my deal
Some creative license is taken here. The mustache is not "fake," but it could be construed as such to enhance the difference between Nick and Jordan. Here again, one uses rap to highlight the difference between the individual and the society that envelopes them.
I don't know if this is something you can use, but I searched a few songs to see if any had lyrics that could help with rewriting this line.
"I never broke one promise, and I know when you're not honest."
Billy Joel- Honesty
"Honesty is such a lonely word,
Everyone is so untrue.
Honesty is hardly ever heard,
And mostly what I need from you."
I don't have much experience with rap, so I just thought of a variation that rhymed and sounded semi-poetic.
"I'm the one who's always honest, while you made an empty promise.
I asked you for the truth, but you can't give me any proof."
Hope this helps!
Everyone are liars
A world full of fire
Although I am honest
the sole individual